Problem: Multiply.
Solution: $77 \times 7$ and $7.7 \times 0.7$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $77 \times 7$. Then we can estimate to place the decimal point in the product of $7.7 \times 0.7$. $\begin{aligned} 77&\\ \underline{ \times 7}&\\ 49}\\ \underline{+490}}\\ 539 \end{aligned}$ Let's estimate to place the decimal in $7.7 \times 0.7$. $\begin{aligned} 7.7 \times 0.7 &\approx 8 \times 0.7\\\\ &\approx \dfrac{8}{1}\times \dfrac{7}{10}\\\\ &\approx \dfrac{56}{10}\\\\ &\approx 5.6 \end{aligned}$ Where can we place the decimal in $539$ to get a product close to $5.6$ ? $5.39 = 7.7 \times 0.7$